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(D) The heat generated in a circuit is given by the formula $H = \frac{V^2}{R} 	imes t$. Since the voltage $V$ and time $t$ are constant,the heat gen

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When the wire is divided into four equal parts and all the four parts are connected in parallel.

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(D) The heat generated in a circuit is given by the formula $H = \frac{V^2}{R} 	imes t$. Since the voltage $V$ and time $t$ are constant,the heat generated is inversely proportional to the resistance $(H \propto \frac{1}{R})$. To maximize heat,we must minimize the total resistance $R$.Let the resistance of the full wire be $R$. $A$: Resistance = $R/2$.$B$: Two parts of $R/2$ in parallel give $R_{eq} = \frac{(R/2) 	imes (R/2)}{(R/2) + (R/2)} = R/4$.$C$: Resistance = $R$.$D$: Four parts of $R/4$ in parallel give $R_{eq} = \frac{R/4}{4} = R/16$.Comparing the resistances: $R/16 < R/4 < R/2 < R$. Since $R/16$ is the smallest resistance,the heat generated is the largest in case $D$.

You are given a resistance wire of length $50 \,cm$ and a battery of negligible resistance. In which of the following cases is the largest amount of heat generated?

Similar Questions

$(a)$ Why are copper or aluminium wires generally used for electrical transmission and distribution purposes?
$(b)$ Two wires,one of copper and the other of manganin,have equal lengths and equal resistances. Which wire is thicker? Given that the resistivity of copper is lower than that of manganin.

The unit of electric power may also be expressed as:

What is the unit of electric current?

Write the $SI$ unit of resistivity.

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